Functioning as a server is a use case. Labelling the desktop / embedded grade hardware as server grade is false marketing in my my opinion. Celeron is a desktop or embedded grade CPU (as per Intel's own classification).
>A server can have any kind of CPU.
You can use any kind of CPU to "serve." From a hardware point of view, there are categories of CPUs that are classified as server grade with specific feature sets. Intel Atom (C series) and Xeon are server grade (again per Intel's classification). The lines between Intel's server and desktop grade CPUs used to be very clear, however they are blurring over time. For example, new Core series CPUs support ECC memory which used to be a server specific feature however they still lack RAS features.
Xeons have support much more memory, have higher core counts, have ECC and RAS, support multi sockets, etc.